This Article 
 Bibliographic References 
 Add to: 
Fault Tolerance in a Class of Sorting Networks
July 1994 (vol. 43 no. 7)
pp. 827-837

The early study of fault tolerance in efficient sorting networks only achieved single-fault tolerance. By eliminating critical comparators, L. Rudolph (1985) presented a 1-fault tolerant design of the balanced sorting network (BSN) at the cost of one redundant stage of N/2 comparators and two permuters external to the network. In this paper, we show, however, that 1-fault tolerance of BSN can be achieved without introducing redundancy and external permuters. Furthermore, we provide solutions to the open question of how to achieve multiple-fault tolerance in BSN. We analyze the problem from a higher-level by introducing a new concept of critical stages, and find that all stages in previous designs are critical. A 2-fault tolerant design of BSN is then discovered after eliminating its critical stages. The new design has a similar network architecture (i.e., a multistage network with the output recirculated back to the input) and the same hardware cost as Rudolph's, but it has many distinguished features. The performance analysis shows that the new designs achieve much higher probabilities of correct sorting in the presence of faulty comparators than the previous reported designs.

[1] L. Rudolph, "A robust sorting network,"IEEE Trans. Comput.(Special issue on sorting), vol. C-34, no. 4, pp. 326-335, Apr. 1985.
[2] K. E. Batcher, "Sorting networks and their applications," inProc. AFIP Spring Joint Comput. Conf., 1968, pp. 307-314.
[3] M. Dowd, Y. Perl, L. Rudolph, and M. Saks, "The balanced sorting network," inProc. ACM Princ. Distrib. Comput., Aug. 1983, pp. 161-172.
[4] H. S. Stone, "Parallel processing with perfect shuffle,"IEEE Trans. Comput., vol. C-20, no. 2, pp. 153-161, Feb. 1971.
[5] F. P. Preparata and J. Vuillemin, "The cube-connected cycle: A versatile network for parallel computation,"Commun. ACM, vol. 24, pp. 300-309, May 1981.
[6] D. Nassimi and S. Sahni, "Parallel permutation and sorting algorithms and a new generalized connection network,"J. ACM, vol. 29, no. 3, pp. 642-667, 1982.
[7] D. E. Knuth,The Art of Computer Programming, Vol. 3, Reading, MA: Addison-Wesley, 1973.
[8] C. D. Thompson, "The VLSI complexity of sorting,"IEEE Trans. Comput., vol. C-32, no. 12, pp. 1171-1184, Dec. 1983.
[9] C. E. Leiserson, "Systolic priority queues,"Proc. CalTech Conf. VLSI, Jan. 1979, pp. 199-224.
[10] S. G. Akl,Parallel Sorting Algorithms. Orlando, FL: Academic, 1985.
[11] T. Y. Feng and C. L. Wu, "Fault-diagnosis for a class of multistage interconnection networks,"IEEE Trans. Comput., vol. C-30, no. 10, pp. 743-758, Oct. 1981.
[12] J. Sun, J. Gecsei, and E. Cerny, "Fault-tolerance in balanced sorting networks,"J. Electron. Testing: Theory and Appl., pp. 31-41, 1990.
[13] J. Sun, E. Cerny, and J. Gecsei, "A robust sorting network for yield improvement," inProc. 1990 IFIP-IEEE Int. Workshop on Defect and Fault-tolerance in VLSI Sys., Grenoble, France, 1990, pp. 217-227.
[14] J. Sun and J. Gecsei, "A multiple-fault tolerant sorting network," inDig. Fault-Tolerant Computing: 21st Int. Symp., June 1991, pp. 274-281.
[15] Y. Choi and M. Malek, "A fault-tolerant systolic sorter,"IEEE Trans. Comput., vol. 37, no. 5, pp. 621-624, May 1988.
[16] S. Liang and S. Kuo, "Concurrent error detection and correction in real-time systolic sorting arrays," inDig. Fault-Tolerant Computing: 20th Int. Symp., June 1990, pp. 434-441.
[17] G. Bilardi, "Merging and sorting networks with the topology of the Omega networks,"IEEE Trans. Comput., vol. 38, no. 10, pp. 1396-1403, Oct. 1989.
[18] A. C. Yao and F. F. Yao, "On fault-tolerant networks for sorting,"SIAM J. Comput., vol. 14, no. 1, pp. 120-128, 1985.
[19] S. Assaf and E. Upfal, "Fault-tolerant sorting network," inProc. of 31st Annu. Symp. Foundations of Comput. Sci., Oct. 1990, pp. 275-284.
[20] T. Leighton, Y. Ma, and C. G. Plaxton, "Highly fault-tolerant sorting circuits," inProc. 32nd Annu. Symp. Foundations of Comput. Sci., 1991, pp. 458-469.
[21] M. R. Samatham and D. K. Pradhan, "The De Bruijn multiprocessor network: A versatile parallel processing and sorting network for VLSI,"IEEE Trans. Comput., vol. 38, no. 4, pp. 567-581, Apr. 1989.

Index Terms:
sorting; comparators (circuits); fault tolerant computing; reliability; parallel processing; fault tolerant computing; fault tolerance; sorting networks; single-fault tolerance; comparators; 1-fault tolerant design; balanced sorting network; 2-fault tolerant design; multistage network.
Jianli Sun, E. Cerny, J. Gecsei, "Fault Tolerance in a Class of Sorting Networks," IEEE Transactions on Computers, vol. 43, no. 7, pp. 827-837, July 1994, doi:10.1109/12.293261
Usage of this product signifies your acceptance of the Terms of Use.